This invention relates to decorrelation of signals in order to improve coding gains of wireless communications; and to a method and a computer program for implementing decorrelation and diversity. In principle, decorrelation in this invention also refers to synthesizing of virtual signals. Data decorrelation is vital in data compression techniques where information needs to be encoded with a few bits. Therefore, decorrelation can be used to reduce dynamic range of signals while bearing the same amount of information. Also, the decorrelated signals possess different signal properties that can be exploited to achieve coding gains in wireless communications. Decorrelation is known to refer to a form of signal processing implemented by software running on a computer system and accepting data from sensors after conversion from analogue to digital form. In this invention, a computer algorithm and apparatus is presented.
Both linearity and stationarity assumptions are used with the present invention. Linearity means that mixtures of signals received by sensors are linear combinations of these signals. Stationarity means that received signals and channels in which they mix remain the same over a sampling time interval for the mixed signals.
Several decorrelation algorithms referred to as instantaneous algorithms can be used to effect decorrelation. Normally, transforms that are energy preserving or not are used. The use of energy preserving transforms for decorrelation avoids information being destroyed and leads to output signals with other useful properties.
In the case that an arbitrary covariance matrix is computed, the problem of finding the decorrelator becomes the orthonormal eigenvector problem. The transformation resulting from the computation of eigenvalues from the covariance matrix is referred to as Karhunen-Loéve transform (KLT).
A method of principal components can also be used to remove signal correlations from discrete elements of a random variable. Several algorithms are known for eigenvalue problems as long as the covariance matrix is given. For example a simple Jacobi method can be used to obtain the eigenvectors of the KLT.
Other methods have recently been introduced that avoid the calculation of covariance matrices but update estimates for each input training vector.
These approaches show some weaknesses in terms of convergence and stability. Mainly, the complexity of computing the covariance matrix or the eigenvectors may need to be incurred in data compression applications, but may not be necessary in achieving coding gains for wireless communications.
In fact discrete Fourier transform (DFT) and fast Fourier transform (FFT) techniques can be used to implement blind decorrelators for wireless communications. However, the problem remains on how to reduce signal errors due to correlation because these transformations are unitary, energy preserving and reciprocal.
In fact, decorrelation results in a reduction in the geometric mean of the new signal variances (eigenvalues) thus improving the coding gain. As a result, if selection combining (SC) is used at the receiver, the signal with the largest variance will be selected leading to decorrelation gains thus, reduction in signal errors. However, even for SC, additional signal errors can be eliminated when the current invention is used.
When the decorrelated signals are combined via equal gain combining (EGG), it has been shown that the decorrelation gains are lost for some signals with high power. For maximal ratio combining (MRC), no additional gains are achieved.
Therefore, the current invention underscores how decorrelation gains can be achieved through blind decorrelation so that signal errors are always reduced for SC and EGC or any other combiner, MRC not being included. We note here that the combining operations for SC, EGC and MRC are known.
Besides, for simplicity of additive signal operations, the current invention does not borrow from DFT, FFT or any other blind decorrelators, but uses binary index transform (BiT). This leads to a simple signal processing algorithm which involves simple binary signal pairing.
It is further noted that blind unitary decorrelators like DFT and FFT may require some form of uniform circular arrays (UCA) and will lead to the less decorrelation gains even when the current invention is used. This is because DFT and FFT operations give almost similar output signals with limited differences. In addition, since eigenvectors developed from the KLT approaches are maximized in a particular direction, equal coding gains will be achieved compared to BiT when eigenvectors obtained from KLT approaches are used with the current invention.
An N branch decorrelator receiver is provided in which decorrelation is performed with a simple addition and subtraction. The decorrelation gains are achieved due to enhanced diversity from virtual antennas assumed to be in the antenna spacing. Virtual signals are the signals in the spacing between the real antennas which are synthesized by computing the principal components (eigenvalue-weighted) of signals in each pair of antennas.
In fact, based on the same, the same decorrelator receiver finds application in processing independent signals, uncorrelated signals and correlated signals to improve plurality of signals before diversity combining is performed.
The present invention seeks to provide an N-branch system consisting of N correlated signals with N uncorrelated signals so as to enhance simple analysis of the figures of merit of the correlated system. Secondly, the present invention seeks to provide additional N(N−1) decorrelated signals to the N correlated signals in order to achieve additional coding gains. Thirdly, the invention also seeks to provide decorrelation in a simple way in order to maintain low complexity at the receiver.